Causal interpretation of the hazard ratio from RCTs when proportional hazards holds

In 2015 I wrote a post about the causal interpretation of hazard ratios estimated in randomised trials, following a paper by Aalen and colleagues. One of the arguments made in that paper was that the hazard ratio does not have a valid interpretation as a causal effect in this setting, even when the proportional hazards assumption holds:

This makes it unclear what the hazard ratio computed for a randomized survival study really means. Note, that this has nothing to do with the fit of the Cox model. The model may fit perfectly in the marginal case with X as the only covariate, but the present problem remains.

With recent discussions on estimands in light of the estimand addendum to ICH E9, I have been thinking more on the argument/claim by Aalen et al.

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Interpreting changes in hazard and hazard ratios

I recently attended a great course by Odd Aalen, Ornulf Borgan, and Hakon Gjessing, based on their book Survival and Event History Analysis: a process point of view. Among the many interesting topics covered was the issue of how to interpret changes in estimated hazard functions, and similarly, changes in hazard ratios comparing two groups of subjects.

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